I tend to view that non-lethal crucifixion used as punishment is itself so painful and degrading that no pre-crux torture is necessary. After all, the person (a slave or nor) is expected to be back working the next day! A person (a woman, shall we say) hanging naked tied to a cross will suffer considerable pain and humiliation for the length of her punishment.
Because crucifixion is the punishment and not intended to permanently main or disfigure, perhaps only a lighter whipping (welts or reddening but the skin is not torn) to the back/buttocks/genitals/breasts is necessary. This is done in public at the punishment site just before she's crucified. Public shaving of her pubic hair to fully display her genitals would be appropriate (as necessary) to increase her humiliation. If the crucifixion is more of a display of her whipped body, i.e., she's more or less standing on a footrest with legs spread and arms tied to a crossbeam, then the whipping or other torture could be more extreme. But if she's actually hanging on the cross by her arms with little support under her body, then crucifixion itself is the punishment. Even standing on tiptoe with arms stretched out along a crossbeam would be quite painful due to muscle cramping after a short time.
My thoughts on this are in the context of living in a society where non-lethal crucifixion is used as a punishment for many lesser crimes (however defined in the society), much along the lines of being publicly displayed in the stocks but with the added humiliation of being exposed fully frontal naked.
How long hanging on the cross? A few hours, perhaps, for a first offense. If she (well, this is crux forums) persists in unacceptable behavior, then additional hours on the cross might help convince her of the error of her ways. Perhaps doubling time on the cross for later offenses: 3 hours first offense, 6 hours second, 12 hours third, 24 hours--well, at this point it may well become lethal. Maybe no whipping with first offense, but varying intensities of whipping for later offenses.
So many variations on this theme!